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/* mpfr_exp -- exponential of a floating-point number
Copyright (C) 1999-2001 Free Software Foundation.
Contributed by the Spaces project.
This file is part of the MPFR Library.
The MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 2.1 of the License, or (at your
option) any later version.
The MPFR Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
License for more details.
You should have received a copy of the GNU Lesser General Public License
along with the MPFR Library; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA. */
#include <stdio.h>
#include "gmp.h"
#include "gmp-impl.h"
#include "mpfr.h"
#include "mpfr-impl.h"
/* #define DEBUG */
extern int mpfr_exp_2 _PROTO((mpfr_ptr, mpfr_srcptr, mp_rnd_t));
extern int mpfr_exp3 _PROTO((mpfr_ptr, mpfr_srcptr, mp_rnd_t));
/* use Brent's formula exp(x) = (1+r+r^2/2!+r^3/3!+...)^(2^K)*2^n
where x = n*log(2)+(2^K)*r
number of operations = O(K+prec(r)/K)
*/
int
mpfr_exp (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode)
{
int expx, precy;
double d;
if (MPFR_IS_NAN(x))
{
MPFR_SET_NAN(y);
return 1;
}
MPFR_CLEAR_NAN(y);
if (MPFR_IS_INF(x))
{
if (MPFR_SIGN(x) > 0)
{
MPFR_SET_INF(y);
if (MPFR_SIGN(y) < 0)
MPFR_CHANGE_SIGN(y);
}
else
{
MPFR_CLEAR_INF(y);
MPFR_SET_ZERO(y);
if (MPFR_SIGN(y) < 0)
MPFR_CHANGE_SIGN(y);
}
return 0;
}
MPFR_CLEAR_INF(y);
if (!MPFR_NOTZERO(x))
{
mpfr_set_ui (y, 1, GMP_RNDN);
return 0;
}
expx = MPFR_EXP(x);
precy = MPFR_PREC(y);
/* result is +Inf when exp(x) >= 2^(__mpfr_emax), i.e.
x >= __mpfr_emax * log(2) */
d = mpfr_get_d (x);
if (d >= (double) __mpfr_emax * LOG2)
{
MPFR_SET_INF(y);
if (MPFR_SIGN(y) < 0)
MPFR_CHANGE_SIGN(y);
return 1; /* overflow */
}
/* result is 0 when exp(x) < 1/2*2^(__mpfr_emin), i.e.
x < (__mpfr_emin-1) * LOG2 */
if (d < ((double) __mpfr_emin - 1.0) * LOG2)
{
MPFR_SET_ZERO(y);
if (MPFR_SIGN(y) < 0)
MPFR_CHANGE_SIGN(y);
return 1; /* underflow */
}
/* if x < 2^(-precy), then exp(x) i.e. gives 1 +/- 1 ulp(1) */
if (expx < -precy)
{
int signx = MPFR_SIGN(x);
mpfr_set_ui (y, 1, rnd_mode);
if (signx > 0 && rnd_mode == GMP_RNDU)
{
mpfr_add_one_ulp (y, rnd_mode);
return 1;
}
else if (signx < 0 && (rnd_mode == GMP_RNDD || rnd_mode == GMP_RNDZ))
{
mpfr_sub_one_ulp (y, rnd_mode);
return -1;
}
return -signx;
}
if (precy > 13000)
return mpfr_exp3 (y, x, rnd_mode); /* O(M(n) log(n)^2) */
else
return mpfr_exp_2 (y, x, rnd_mode); /* O(n^(1/3) M(n)) */
}
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